8 sides 17 sides. x = 72

Transcription

1 GEOMETRY Chapter 7 Review Quadrilaterals Name: Hour: Date: SECTION 1: State whether each polygon is equilateral, equiangular, or regular. 1) 2) 3) equilateral regular equiangular SECTION 2: Calculate the sum of the interior angle measures of the polygon. 4) 5) SECTION 3: Determine how many sides the polygon would have based on sum of its interior angle measures. 8 sides 17 sides 6) ) 2700 SECTION 4: Use the diagram to answer each question. 8) What is the sum of the exterior angles of this polygon? 9) What is the value of x in this diagram? SECTION 5: Use the given information to calculate the value of x. 6) 7) x = x = 79 x = 8 SECTION 6: Use the diagram to fill in each blank about parallelogram EFGH. Give a reason (theorem or definition) for each answer. 8) HEF. Reason: EF 9) HG. Reason: GD HGF Opp. Angles of a Parallelogram Thm. Opp. Sides of a Parallelogram Thm. 10) ED. Reason: GF Diagonals of a Parallelogram Thm. Definition of Parallelogram 11) HE. Reason: EHG EFG. Consec. Angles of a Parallelogram Thm. 12) HGF is supplementary to and. Reason:

2 SECTION 7: Given that PQRS is a parallelogram, find the values of x and y. 13) 14) x = 3 and y = 9 x = 8 and y = 98 SECTION 8: Decide if you ve been given enough information to show that the quadrilateral is a parallelogram. Explain your reasoning. 15) 16) 17) YES. Opp. Sides of a Parallelogram Converse NO. Not enough information. YES. Alt. Int. Angles Converse and Definition of Parallelogram. SECTION 9: Write a two column proof. 18) GIVEN: AE = 23, BE = 18, CE = 23, and DE = 18 PROVE: ABCD is a parallelogram STATEMENTS REASONS AE = 23, BE = 18, CE = 23, DE = 18 1) 1) AE = CE and BE = DE 2) 2) AE CE and BE DE Given 3) 3) ABCD is a parallelogram Transitive Property of Equality Definition of Congruent Segments Diagonals of a Parallelogram Converse 4) 4) SECTION 10: Decide if the statement is always, sometimes, or never true. sometimes always always never 19) A rectangle is a square. 20) A square is a rhombus. 21) A trapezoid is a quadrilateral. 22) A kite is a parallelogram.

3 SECTION 11: For rhombus RHMB, decide whether or not each statement is true. Explain your answer with a definition, theorem, etc. TRUE. Definition of Rhombus 23) BR BM TRUE. Bisected Angles of a Rhombus Theorem TRUE. Perpendicular Diagonals of a Rhombus Theorem 24) RBS MBS 25) RSH is a right angle SECTION 12: For rectangle RCTN, decide whether or not each statement is true. Explain your answer with a definition, theorem, etc. TRUE. Diagonals of a Rectangle Theorem 26) RT NC NOT NECESSARILY TRUE. (Would be true if it were a square.) TRUE. Definition of Rectangle 27) RCG TCG 28) RNT is a right angle SECTION 13: Find the value of x based on the information provided. 29) 30) 31) x = 30 x = 10 x = 19 SECTION 14: Find the angles measures of the kite. 32) 33) E = 118 K = 50 I = 124 K = 80

4 SECTION 15: Find the missing angle measures of the trapezoids. 34) 35) 36) B = 53, D = 127, C = 127 D = 89, C = 48 SECTION 16: Find the length of the midsegment. B = 108, D = 72, C = 72 37) 38) RT = 10.5 RT = 20 SECTION 17: Identify each quadrilateral. Use the most specific name possible. 39) 40) 41) Square Parallelogram Isosceles Trapezoid SECTION 18: What kind of quadrilateral is ABCD? Use the most specific name possible. Show your work and justify your answer. 42) A(4, 8), B(1, 5), C(7, 5), D(4, 1) KITE. Method 1: Use the Distance Formula to show that there are two pairs of consecutive congruent sides. D A B Method 2: Use the Slope Formula to show that the diagonals are perpendicular and that none of the sides are parallel. C

5 SECTION 19: Find the area of each figure. 43) 44) 45) A = 147 units 2 A = 256 cm 2 A = 76.5 m 2 46) 47) 48) A = 504 ft 2 A = 3,400 yd 2 A = 630 km 2 49) 50) 51) A = 4,545 in 2 A = 160 units 2 A = 1,296 mi 2 SECTION 20: Find the area of each polygon. 52) Triangle ABC 53) Kite DEFG 54) Parallelogram HIJK A = 35 units 2 A = 40 units 2 A = 24 units 2

6 SECTION 21: Find the area of the shaded region. 55) 56) 57) A = 124 cm 2 A = 40 m 2 A = 120 ft 2 SECTION 22: Circle the letter of each characteristic that applies to the given quadrilaterals. 58) Parallelogram 59) Rhombus 60) Rectangle 61) Square A) Diagonals are perpendicular. B) Diagonals bisect the opposite angles. C) Diagonals are congruent. D) Diagonals bisect each other. E) Only one pair of opposite sides are parallel. F) Two pairs of opposite sides are parallel. G) Two pairs of opposite sides are congruent. H) Two pairs of consecutive sides are congruent. I) Only one pair of opposite sides is congruent. 62) Trapezoid 63) Isosceles Trapezoid J) Only two pairs of consecutive angles are supplementary. K) Every pair of consecutive angles is supplementary. L) Only one pair of opposite angles is congruent. M) Two pairs of opposite angles are congruent. 64) Kite